#include "inttypes.h"
#include "ntt.h"
#include "params.h"

/* Precomputed NTT contants generated by Pari/GP script as follows:
 *
 * For n = 512:
 *
 * brv = [0,256,128,384,64,320,192,448,32,288,160,416,96,352,224,480,16,272,144,400,80,336,208,464,48,304,176,432,112,368,240,496,8,
 *        264,136,392,72,328,200,456,40,296,168,424,104,360,232,488,24,280,152,408,88,344,216,472,56,312,184,440,120,376,248,504,4,
 *        260,132,388,68,324,196,452,36,292,164,420,100,356,228,484,20,276,148,404,84,340,212,468,52,308,180,436,116,372,244,500,12,
 *        268,140,396,76,332,204,460,44,300,172,428,108,364,236,492,28,284,156,412,92,348,220,476,60,316,188,444,124,380,252,508,2,
 *        258,130,386,66,322,194,450,34,290,162,418,98,354,226,482,18,274,146,402,82,338,210,466,50,306,178,434,114,370,242,498,10,
 *        266,138,394,74,330,202,458,42,298,170,426,106,362,234,490,26,282,154,410,90,346,218,474,58,314,186,442,122,378,250,506,6,
 *        262,134,390,70,326,198,454,38,294,166,422,102,358,230,486,22,278,150,406,86,342,214,470,54,310,182,438,118,374,246,502,14,
 *        270,142,398,78,334,206,462,46,302,174,430,110,366,238,494,30,286,158,414,94,350,222,478,62,318,190,446,126,382,254,510,1,
 *        257,129,385,65,321,193,449,33,289,161,417,97,353,225,481,17,273,145,401,81,337,209,465,49,305,177,433,113,369,241,497,9,
 *        265,137,393,73,329,201,457,41,297,169,425,105,361,233,489,25,281,153,409,89,345,217,473,57,313,185,441,121,377,249,505,5,
 *        261,133,389,69,325,197,453,37,293,165,421,101,357,229,485,21,277,149,405,85,341,213,469,53,309,181,437,117,373,245,501,13,
 *        269,141,397,77,333,205,461,45,301,173,429,109,365,237,493,29,285,157,413,93,349,221,477,61,317,189,445,125,381,253,509,3,
 *        259,131,387,67,323,195,451,35,291,163,419,99,355,227,483,19,275,147,403,83,339,211,467,51,307,179,435,115,371,243,499,11,
 *        267,139,395,75,331,203,459,43,299,171,427,107,363,235,491,27,283,155,411,91,347,219,475,59,315,187,443,123,379,251,507,7,
 *        263,135,391,71,327,199,455,39,295,167,423,103,359,231,487,23,279,151,407,87,343,215,471,55,311,183,439,119,375,247,503,15,
 *        271,143,399,79,335,207,463,47,303,175,431,111,367,239,495,31,287,159,415,95,351,223,479,63,319,191,447,127,383,255,511
 * n = 1024; q = 12289; mont=2^18
 * g=0; for(i=2,q-1,if(znorder(Mod(i,q)) == 2*n, g=Mod(i,q); break))
 * omegas_bitrev_montgomery = lift(vector(n/2, i, g^(brv[i])*mont))
 * omegas_inv_bitrev_montgomery = lift(vector(n/2, i, (g^2)^(-brv[2*(i-1)+1])*mont))
 * psis_bitrev_montgomery = lift(vector(n, i, g^(brv[i])*mont))
 * psis_inv_montgomery = lift(vector(n, i, g^(-(i-1))/n*mont))
 *
 *
 *  For n = 1024:
 *
 * brv = [0,512,256,768,128,640,384,896,64,576,320,832,192,704,448,960,32,544,288,800,160,672,416,928,96,608,352,864,224,736,480,992, \
 *        16,528,272,784,144,656,400,912,80,592,336,848,208,720,464,976,48,560,304,816,176,688,432,944,112,624,368,880,240,752,496,1008, \
 *        8,520,264,776,136,648,392,904,72,584,328,840,200,712,456,968,40,552,296,808,168,680,424,936,104,616,360,872,232,744,488,1000, \
 *        24,536,280,792,152,664,408,920,88,600,344,856,216,728,472,984,56,568,312,824,184,696,440,952,120,632,376,888,248,760,504,1016, \
 *        4,516,260,772,132,644,388,900,68,580,324,836,196,708,452,964,36,548,292,804,164,676,420,932,100,612,356,868,228,740,484,996, \
 *        20,532,276,788,148,660,404,916,84,596,340,852,212,724,468,980,52,564,308,820,180,692,436,948,116,628,372,884,244,756,500,1012, \
 *        12,524,268,780,140,652,396,908,76,588,332,844,204,716,460,972,44,556,300,812,172,684,428,940,108,620,364,876,236,748,492,1004, \
 *        28,540,284,796,156,668,412,924,92,604,348,860,220,732,476,988,60,572,316,828,188,700,444,956,124,636,380,892,252,764,508,1020, \
 *        2,514,258,770,130,642,386,898,66,578,322,834,194,706,450,962,34,546,290,802,162,674,418,930,98,610,354,866,226,738,482,994, \
 *        18,530,274,786,146,658,402,914,82,594,338,850,210,722,466,978,50,562,306,818,178,690,434,946,114,626,370,882,242,754,498,1010, \
 *        10,522,266,778,138,650,394,906,74,586,330,842,202,714,458,970,42,554,298,810,170,682,426,938,106,618,362,874,234,746,490,1002, \
 *        26,538,282,794,154,666,410,922,90,602,346,858,218,730,474,986,58,570,314,826,186,698,442,954,122,634,378,890,250,762,506,1018, \
 *        6,518,262,774,134,646,390,902,70,582,326,838,198,710,454,966,38,550,294,806,166,678,422,934,102,614,358,870,230,742,486,998, \
 *        22,534,278,790,150,662,406,918,86,598,342,854,214,726,470,982,54,566,310,822,182,694,438,950,118,630,374,886,246,758,502,1014, \
 *        14,526,270,782,142,654,398,910,78,590,334,846,206,718,462,974,46,558,302,814,174,686,430,942,110,622,366,878,238,750,494,1006, \
 *        30,542,286,798,158,670,414,926,94,606,350,862,222,734,478,990,62,574,318,830,190,702,446,958,126,638,382,894,254,766,510,1022, \
 *        1,513,257,769,129,641,385,897,65,577,321,833,193,705,449,961,33,545,289,801,161,673,417,929,97,609,353,865,225,737,481,993, \
 *        17,529,273,785,145,657,401,913,81,593,337,849,209,721,465,977,49,561,305,817,177,689,433,945,113,625,369,881,241,753,497,1009, \
 *        9,521,265,777,137,649,393,905,73,585,329,841,201,713,457,969,41,553,297,809,169,681,425,937,105,617,361,873,233,745,489,1001, \
 *        25,537,281,793,153,665,409,921,89,601,345,857,217,729,473,985,57,569,313,825,185,697,441,953,121,633,377,889,249,761,505,1017, \
 *        5,517,261,773,133,645,389,901,69,581,325,837,197,709,453,965,37,549,293,805,165,677,421,933,101,613,357,869,229,741,485,997, \
 *        21,533,277,789,149,661,405,917,85,597,341,853,213,725,469,981,53,565,309,821,181,693,437,949,117,629,373,885,245,757,501,1013, \
 *        13,525,269,781,141,653,397,909,77,589,333,845,205,717,461,973,45,557,301,813,173,685,429,941,109,621,365,877,237,749,493,1005, \
 *        29,541,285,797,157,669,413,925,93,605,349,861,221,733,477,989,61,573,317,829,189,701,445,957,125,637,381,893,253,765,509,1021, \
 *        3,515,259,771,131,643,387,899,67,579,323,835,195,707,451,963,35,547,291,803,163,675,419,931,99,611,355,867,227,739,483,995, \
 *        19,531,275,787,147,659,403,915,83,595,339,851,211,723,467,979,51,563,307,819,179,691,435,947,115,627,371,883,243,755,499,1011, \
 *        11,523,267,779,139,651,395,907,75,587,331,843,203,715,459,971,43,555,299,811,171,683,427,939,107,619,363,875,235,747,491,1003, \
 *        27,539,283,795,155,667,411,923,91,603,347,859,219,731,475,987,59,571,315,827,187,699,443,955,123,635,379,891,251,763,507,1019, \
 *        7,519,263,775,135,647,391,903,71,583,327,839,199,711,455,967,39,551,295,807,167,679,423,935,103,615,359,871,231,743,487,999, \
 *        23,535,279,791,151,663,407,919,87,599,343,855,215,727,471,983,55,567,311,823,183,695,439,951,119,631,375,887,247,759,503,1015, \
 *        15,527,271,783,143,655,399,911,79,591,335,847,207,719,463,975,47,559,303,815,175,687,431,943,111,623,367,879,239,751,495,1007, \
 *        31,543,287,799,159,671,415,927,95,607,351,863,223,735,479,991,63,575,319,831,191,703,447,959,127,639,383,895,255,767,511,1023]
 * 
 * n = 1024; q = 12289; mont=2^18
 * g=0; for(i=2,q-1,if(znorder(Mod(i,q)) == 2*n, g=Mod(i,q); break))
 * omegas_bitrev_montgomery = lift(vector(n/2, i, g^(brv[i])*mont))
 * omegas_inv_bitrev_montgomery = lift(vector(n/2, i, (g^2)^(-brv[2*(i-1)+1])*mont))
 * psis_bitrev_montgomery = lift(vector(n, i, g^(brv[i])*mont))
 * psis_inv_montgomery = lift(vector(n, i, g^(-(i-1))/n*mont))
*/


#if (NEWHOPE_N == 512)
/************************************************************
* Name:        omegas_bitrev_montgomery
*
* Description: Contains powers of nth root of unity in Montgomery 
*              domain with R=2^18 in bit-reversed order
************************************************************/
uint16_t omegas_bitrev_montgomery[NEWHOPE_N/2] = {
  4075,5315,7965,7373,522,10120,9027,5079,2344,1278,1973,5574,1018,6364,11248,8775,
  7500,7822,5537,4749,8500,12142,5456,7840,5445,3860,4536,11239,6171,8471,2683,11099,
  10561,400,6137,7341,5415,8646,6136,5862,5529,5206,56,9090,8724,11635,1702,10302,
  5339,6843,6093,3710,316,382,11821,8301,10930,5435,11035,973,8291,10256,8410,1922,
  12097,10968,10240,4912,4698,5057,7509,8844,8807,11502,5468,1010,9162,8120,2920,5241,
  6055,8953,677,5874,2766,10966,12237,9115,12138,10162,3957,2839,6383,2505,11858,1579,
  9026,3600,6077,4624,11868,4080,6068,3602,605,9987,504,8076,4782,6403,3029,6695,
  11184,142,5681,8812,2844,3438,8077,975,58,12048,1003,8757,885,6281,1956,5009,
  12225,3656,11606,9830,1566,5782,2503,2948,7032,3834,5919,4433,3054,6803,9166,1747,
  10211,11177,4322,1958,922,11848,4079,11231,4046,11580,1319,9139,6224,835,8049,8719,
  7105,1200,6122,9734,3956,1360,6119,5297,4298,3329,168,2692,1594,10327,5106,6328,
  3728,8240,5990,11130,948,1146,10885,325,8212,4016,8527,2919,295,6190,652,5766,
  11713,8326,6142,2447,1805,2882,10238,1954,1843,9928,4115,3030,2908,12071,8760,3434,
  5876,2281,2031,5333,8298,8320,12133,2767,11836,5908,11871,8517,6860,7515,10996,4737,
  2500,10800,5942,1583,11026,12240,5915,10806,1815,5383,1512,11939,2057,6920,9087,7796,
  8974,426,4754,1858,8532,10314,11942,2925,174,11566,3009,1693,2655,6554,5868,2738,
};

/************************************************************
* Name:        omegas_inv_bitrev_montgomery
*
* Description: Contains inverses of powers of nth root of unity 
*              in Montgomery domain with R=2^18 in bit-reversed order
************************************************************/
uint16_t omegas_inv_bitrev_montgomery[NEWHOPE_N/2] = {
  4075,6974,4916,4324,7210,3262,2169,11767,3514,1041,5925,11271,6715,10316,11011,9945,
  1190,9606,3818,6118,1050,7753,8429,6844,4449,6833,147,3789,7540,6752,4467,4789,
  10367,3879,2033,3998,11316,1254,6854,1359,3988,468,11907,11973,8579,6196,5446,6950,
  1987,10587,654,3565,3199,12233,7083,6760,6427,6153,3643,6874,4948,6152,11889,1728,
  7280,10333,6008,11404,3532,11286,241,12231,11314,4212,8851,9445,3477,6608,12147,1105,
  5594,9260,5886,7507,4213,11785,2302,11684,8687,6221,8209,421,7665,6212,8689,3263,
  10710,431,9784,5906,9450,8332,2127,151,3174,52,1323,9523,6415,11612,3336,6234,
  7048,9369,4169,3127,11279,6821,787,3482,3445,4780,7232,7591,7377,2049,1321,192,
  9551,6421,5735,9634,10596,9280,723,12115,9364,347,1975,3757,10431,7535,11863,3315,
  4493,3202,5369,10232,350,10777,6906,10474,1483,6374,49,1263,10706,6347,1489,9789,
  7552,1293,4774,5429,3772,418,6381,453,9522,156,3969,3991,6956,10258,10008,6413,
  8855,3529,218,9381,9259,8174,2361,10446,10335,2051,9407,10484,9842,6147,3963,576,
  6523,11637,6099,11994,9370,3762,8273,4077,11964,1404,11143,11341,1159,6299,4049,8561,
  5961,7183,1962,10695,9597,12121,8960,7991,6992,6170,10929,8333,2555,6167,11089,5184,
  3570,4240,11454,6065,3150,10970,709,8243,1058,8210,441,11367,10331,7967,1112,2078,
  10542,3123,5486,9235,7856,6370,8455,5257,9341,9786,6507,10723,2459,683,8633,64,
};

/************************************************************
* Name:        psis_bitrev_montgomery
*
* Description: Contains powers of nth root of -1 in Montgomery 
*              domain with R=2^18 in bit-reversed order
************************************************************/
uint16_t psis_bitrev_montgomery[NEWHOPE_N] = {
  4075,5315,7965,7373,522,10120,9027,5079,2344,1278,1973,5574,1018,6364,11248,8775,
  7500,7822,5537,4749,8500,12142,5456,7840,5445,3860,4536,11239,6171,8471,2683,11099,
  10561,400,6137,7341,5415,8646,6136,5862,5529,5206,56,9090,8724,11635,1702,10302,
  5339,6843,6093,3710,316,382,11821,8301,10930,5435,11035,973,8291,10256,8410,1922,
  12097,10968,10240,4912,4698,5057,7509,8844,8807,11502,5468,1010,9162,8120,2920,5241,
  6055,8953,677,5874,2766,10966,12237,9115,12138,10162,3957,2839,6383,2505,11858,1579,
  9026,3600,6077,4624,11868,4080,6068,3602,605,9987,504,8076,4782,6403,3029,6695,
  11184,142,5681,8812,2844,3438,8077,975,58,12048,1003,8757,885,6281,1956,5009,
  12225,3656,11606,9830,1566,5782,2503,2948,7032,3834,5919,4433,3054,6803,9166,1747,
  10211,11177,4322,1958,922,11848,4079,11231,4046,11580,1319,9139,6224,835,8049,8719,
  7105,1200,6122,9734,3956,1360,6119,5297,4298,3329,168,2692,1594,10327,5106,6328,
  3728,8240,5990,11130,948,1146,10885,325,8212,4016,8527,2919,295,6190,652,5766,
  11713,8326,6142,2447,1805,2882,10238,1954,1843,9928,4115,3030,2908,12071,8760,3434,
  5876,2281,2031,5333,8298,8320,12133,2767,11836,5908,11871,8517,6860,7515,10996,4737,
  2500,10800,5942,1583,11026,12240,5915,10806,1815,5383,1512,11939,2057,6920,9087,7796,
  8974,426,4754,1858,8532,10314,11942,2925,174,11566,3009,1693,2655,6554,5868,2738,
  11796,8193,9908,5444,10911,1912,7952,435,404,7644,11224,10146,7012,11121,11082,9041,
  9723,2187,9867,6250,3646,9852,6267,2987,8509,875,4976,10682,8005,5088,7278,11287,
  9223,27,3763,10849,11272,7404,5084,10657,8146,4714,12047,10752,2678,3704,545,7270,
  1067,5101,442,2401,390,11516,3778,8456,1045,9430,9808,5012,9377,6591,11935,4861,
  7852,3,3149,12129,12176,4919,10123,3915,3636,7351,2704,5291,1663,1777,1426,7635,
  1484,7394,2780,7094,8236,2645,7247,2305,2847,7875,7917,10115,10600,8925,4057,3271,
  9273,243,9289,11618,3136,5191,8889,9890,11869,5559,10111,10745,11813,8758,4905,3985,
  9603,9042,3978,9320,3510,5332,9424,2370,9405,11136,2249,8241,10659,10163,9103,6882,
  10810,1,5146,4043,8155,5736,11567,1305,1212,10643,9094,5860,8747,8785,8668,2545,
  4591,6561,5023,6461,10938,4978,6512,8961,949,2625,2639,7468,11726,2975,9545,9283,
  3091,81,11289,7969,9238,9923,2963,7393,12149,1853,11563,7678,8034,11112,1635,9521,
  3201,3014,1326,7203,1170,9970,11334,790,3135,3712,4846,2747,3553,7484,11227,2294,
  11267,9,9447,11809,11950,2468,5791,11745,10908,9764,8112,3584,4989,5331,4278,10616,
  4452,9893,8340,8993,130,7935,9452,6915,8541,11336,11462,5767,7222,2197,12171,9813,
  3241,729,3289,10276,9408,3284,2089,5092,11029,4388,5755,7657,10861,1696,2426,11955,
  4231,2548,11934,3382,10530,3707,3694,7110,3637,8830,6747,145,7399,5911,2731,8357,
};

/************************************************************
* Name:         psis_inv_montgomery
*
* Description: Contains inverses of powers of nth  root of -1 
*              divided by n in Montgomery domain with R=2^18
************************************************************/
uint16_t psis_inv_montgomery[NEWHOPE_N] = {
  512,3944,4267,5411,9615,5900,3205,6063,9261,2021,3087,4770,1029,1590,343,530,
  8307,4273,2769,9617,923,7302,4404,2434,1468,9004,8682,11194,2894,11924,5061,8071,
  1687,10883,8755,7724,11111,6671,7800,6320,2600,6203,4963,6164,9847,6151,11475,10243,
  3825,11607,1275,3869,425,5386,4238,9988,5509,11522,10029,7937,3343,6742,9307,10440,
  11295,3480,3765,1160,1255,4483,8611,9687,11063,3229,7784,9269,6691,7186,10423,10588,
  11667,11722,3889,12100,9489,12226,3163,12268,9247,12282,11275,4094,11951,5461,8080,10013,
  10886,7434,7725,2478,2575,826,9051,8468,3017,6919,5102,10499,5797,7596,10125,2532,
  3375,844,1125,8474,375,6921,125,2307,4138,769,9572,8449,7287,11009,2429,7766,
  4906,6685,9828,10421,3276,7570,1092,10716,364,3572,8314,5287,10964,9955,7751,11511,
  6680,3837,6323,1279,6204,8619,2068,2873,8882,5054,7057,5781,10545,1927,3515,8835,
  5268,2945,1756,5078,8778,5789,2926,6026,9168,6105,3056,2035,5115,8871,1705,2957,
  8761,5082,11113,1694,11897,4661,8062,5650,10880,10076,7723,7455,10767,2485,3589,9021,
  9389,3007,7226,9195,6505,3065,10361,5118,7550,1706,6613,4665,10397,1555,7562,8711,
  6617,7000,6302,10526,6197,7605,6162,2535,2054,845,4781,4378,5690,9652,5993,11410,
  6094,11996,10224,8095,3408,10891,1136,11823,4475,3941,5588,5410,5959,9996,10179,3332,
  3393,5207,1131,5832,377,1944,4222,648,9600,216,3200,72,5163,24,1721,8,
  4670,4099,5653,9559,10077,11379,3359,3793,5216,9457,5835,11345,1945,7878,8841,2626,
  2947,9068,9175,7119,11251,2373,11943,791,3981,4360,1327,9646,8635,11408,11071,7899,
  11883,2633,3961,4974,9513,1658,3171,4649,1057,5646,8545,1882,11041,8820,11873,2940,
  8054,980,6781,4423,10453,9667,11677,11415,12085,3805,12221,9461,8170,7250,10916,6513,
  7735,2171,10771,4820,11783,5703,8024,1901,6771,4730,2257,5673,8945,1891,7078,8823,
  10552,2941,11710,9173,12096,7154,4032,6481,1344,10353,448,3451,8342,9343,6877,11307,
  10485,3769,3495,9449,1165,7246,8581,10608,11053,3536,11877,5275,3959,9951,5416,3317,
  9998,5202,7429,1734,10669,578,11749,4289,12109,5526,12229,1842,12269,614,8186,4301,
  6825,5530,2275,10036,8951,11538,7080,3846,2360,1282,4883,8620,5724,11066,1908,7785,
  636,2595,212,865,4167,8481,1389,2827,463,9135,8347,3045,10975,1015,11851,8531,
  12143,6940,8144,10506,6811,3502,10463,9360,7584,3120,2528,1040,4939,4443,9839,1481,
  7376,4590,6555,1530,2185,510,8921,170,7070,4153,6453,9577,2151,11385,717,3795,
  239,1265,4176,4518,1392,1506,464,502,4251,8360,1417,6883,8665,10487,11081,7592,
  7790,6627,6693,2209,2231,8929,4840,11169,9806,3723,7365,1241,2455,4510,9011,9696,
  7100,3232,6463,9270,10347,3090,3449,1030,5246,8536,5845,11038,10141,11872,11573,12150,
  7954,4050,10844,1350,7711,450,10763,150,7684,50,10754,4113,7681,1371,10753,457,
};

#elif (NEWHOPE_N == 1024)
/************************************************************
* Name:        omegas_bitrev_montgomery
*
* Description: Contains powers of nth root of unity in Montgomery 
*              domain with R=2^18 in bit-reversed order
************************************************************/
uint16_t omegas_bitrev_montgomery[NEWHOPE_N/2] = {
  4075,6974,7373,7965,3262,5079,522,2169,6364,1018,1041,8775,2344,11011,5574,1973,
  4536,1050,6844,3860,3818,6118,2683,1190,4789,7822,7540,6752,5456,4449,3789,12142,
  11973,382,3988,468,6843,5339,6196,3710,11316,1254,5435,10930,3998,10256,10367,3879,
  11889,1728,6137,4948,5862,6136,3643,6874,8724,654,10302,1702,7083,6760,56,3199,
  9987,605,11785,8076,5594,9260,6403,4782,6212,4624,9026,8689,4080,11868,6221,3602,
  975,8077,8851,9445,5681,3477,1105,142,241,12231,1003,3532,5009,1956,6008,11404,
  7377,2049,10968,12097,7591,5057,3445,4780,2920,7048,3127,8120,11279,6821,11502,8807,
  12138,2127,2839,3957,431,1579,6383,9784,5874,677,3336,6234,2766,1323,9115,12237,
  2031,6956,6413,2281,3969,3991,12133,9522,4737,10996,4774,5429,11871,3772,453,5908,
  2882,1805,2051,1954,11713,3963,2447,6142,8174,3030,1843,2361,12071,2908,3529,3434,
  3202,7796,2057,5369,11939,1512,6906,10474,11026,49,10806,5915,1489,9789,5942,10706,
  10431,7535,426,8974,3757,10314,9364,347,5868,9551,9634,6554,10596,9280,11566,174,
  2948,2503,6507,10723,11606,2459,64,3656,8455,5257,5919,7856,1747,9166,5486,9235,
  6065,835,3570,4240,11580,4046,10970,9139,1058,8210,11848,922,7967,1958,10211,1112,
  3728,4049,11130,5990,1404,325,948,11143,6190,295,11637,5766,8212,8273,2919,8527,
  6119,6992,8333,1360,2555,6167,1200,7105,7991,3329,9597,12121,5106,5961,10695,10327,
  3051,9923,4896,9326,81,3091,1000,7969,4611,726,1853,12149,4255,11112,2768,10654,
  1062,2294,3553,4805,2747,4846,8577,9154,1170,2319,790,11334,9275,9088,1326,5086,
  9094,6429,11077,10643,3504,3542,8668,9744,1479,1,8246,7143,11567,10984,4134,5736,
  4978,10938,5777,8961,4591,5728,6461,5023,9650,7468,949,9664,2975,11726,2744,9283,
  10092,5067,12171,2476,3748,11336,6522,827,9452,5374,12159,7935,3296,3949,9893,4452,
  10908,2525,3584,8112,8011,10616,4989,6958,11809,9447,12280,1022,11950,9821,11745,5791,
  5092,2089,9005,2881,3289,2013,9048,729,7901,1260,5755,4632,11955,2426,10593,1428,
  4890,5911,3932,9558,8830,3637,5542,145,5179,8595,3707,10530,355,3382,4231,9741,
  1207,9041,7012,1168,10146,11224,4645,11885,10911,10377,435,7952,4096,493,9908,6845,
  6039,2422,2187,9723,8643,9852,9302,6022,7278,1002,4284,5088,1607,7313,875,8509,
  9430,1045,2481,5012,7428,354,6591,9377,11847,2401,1067,7188,11516,390,8511,8456,
  7270,545,8585,9611,12047,1537,4143,4714,4885,1017,5084,1632,3066,27,1440,8526,
  9273,12046,11618,9289,3400,9890,3136,7098,8758,11813,7384,3985,11869,6730,10745,10111,
  2249,4048,2884,11136,2126,1630,9103,5407,2686,9042,2969,8311,9424,9919,8779,5332,
  10626,1777,4654,10863,7351,3636,9585,5291,8374,2166,4919,12176,9140,12129,7852,12286,
  4895,10805,2780,5195,2305,7247,9644,4053,10600,3364,3271,4057,4414,9442,7917,2174};

/************************************************************
* Name:         omegas_inv_bitrev_montgomery
*
* Description: Contains inverses of powers of nth root of unity 
*              in Montgomery domain with R=2^18 in bit-reversed order
************************************************************/
uint16_t omegas_inv_bitrev_montgomery[NEWHOPE_N/2] = {
  4075,5315,4324,4916,10120,11767,7210,9027,10316,6715,1278,9945,3514,11248,11271,5925,
  147,8500,7840,6833,5537,4749,4467,7500,11099,9606,6171,8471,8429,5445,11239,7753,
  9090,12233,5529,5206,10587,1987,11635,3565,5415,8646,6153,6427,7341,6152,10561,400,
  8410,1922,2033,8291,1359,6854,11035,973,8579,6093,6950,5446,11821,8301,11907,316,
  52,3174,10966,9523,6055,8953,11612,6415,2505,5906,10710,11858,8332,9450,10162,151,
  3482,787,5468,1010,4169,9162,5241,9369,7509,8844,7232,4698,192,1321,10240,4912,
  885,6281,10333,7280,8757,11286,58,12048,12147,11184,8812,6608,2844,3438,4212,11314,
  8687,6068,421,8209,3600,3263,7665,6077,7507,5886,3029,6695,4213,504,11684,2302,
  1962,1594,6328,7183,168,2692,8960,4298,5184,11089,6122,9734,10929,3956,5297,6170,
  3762,9370,4016,4077,6523,652,11994,6099,1146,11341,11964,10885,6299,1159,8240,8561,
  11177,2078,10331,4322,11367,441,4079,11231,3150,1319,8243,709,8049,8719,11454,6224,
  3054,6803,3123,10542,4433,6370,7032,3834,8633,12225,9830,683,1566,5782,9786,9341,
  12115,723,3009,1693,5735,2655,2738,6421,11942,2925,1975,8532,3315,11863,4754,1858,
  1583,6347,2500,10800,6374,1483,12240,1263,1815,5383,10777,350,6920,10232,4493,9087,
  8855,8760,9381,218,9928,10446,9259,4115,6147,9842,8326,576,10335,10238,10484,9407,
  6381,11836,8517,418,6860,7515,1293,7552,2767,156,8298,8320,10008,5876,5333,10258,
  10115,4372,2847,7875,8232,9018,8925,1689,8236,2645,5042,9984,7094,9509,1484,7394,
  3,4437,160,3149,113,7370,10123,3915,6998,2704,8653,4938,1426,7635,10512,1663,
  6957,3510,2370,2865,3978,9320,3247,9603,6882,3186,10659,10163,1153,9405,8241,10040,
  2178,1544,5559,420,8304,4905,476,3531,5191,9153,2399,8889,3000,671,243,3016,
  3763,10849,12262,9223,10657,7205,11272,7404,7575,8146,10752,242,2678,3704,11744,5019,
  3833,3778,11899,773,5101,11222,9888,442,2912,5698,11935,4861,7277,9808,11244,2859,
  3780,11414,4976,10682,7201,8005,11287,5011,6267,2987,2437,3646,2566,10102,9867,6250,
  5444,2381,11796,8193,4337,11854,1912,1378,404,7644,1065,2143,11121,5277,3248,11082,
  2548,8058,8907,11934,1759,8582,3694,7110,12144,6747,8652,3459,2731,8357,6378,7399,
  10861,1696,9863,334,7657,6534,11029,4388,11560,3241,10276,9000,9408,3284,10200,7197,
  6498,544,2468,339,11267,9,2842,480,5331,7300,1673,4278,4177,8705,9764,1381,
  7837,2396,8340,8993,4354,130,6915,2837,11462,5767,953,8541,9813,118,7222,2197,
  3006,9545,563,9314,2625,11340,4821,2639,7266,5828,6561,7698,3328,6512,1351,7311,
  6553,8155,1305,722,5146,4043,12288,10810,2545,3621,8747,8785,1646,1212,5860,3195,
  7203,10963,3201,3014,955,11499,9970,11119,3135,3712,7443,9542,7484,8736,9995,11227,
  1635,9521,1177,8034,140,10436,11563,7678,4320,11289,9198,12208,2963,7393,2366,9238};

/************************************************************
* Name:        psis_bitrev_montgomery
*
* Description: Contains powers of nth root of -1 in Montgomery 
*              domain with R=2^18 in bit-reversed order
************************************************************/
uint16_t psis_bitrev_montgomery[NEWHOPE_N] = {
  4075,6974,7373,7965,3262,5079,522,2169,6364,1018,1041,8775,2344,11011,5574,1973,
  4536,1050,6844,3860,3818,6118,2683,1190,4789,7822,7540,6752,5456,4449,3789,12142,
  11973,382,3988,468,6843,5339,6196,3710,11316,1254,5435,10930,3998,10256,10367,3879,
  11889,1728,6137,4948,5862,6136,3643,6874,8724,654,10302,1702,7083,6760,56,3199,
  9987,605,11785,8076,5594,9260,6403,4782,6212,4624,9026,8689,4080,11868,6221,3602,
  975,8077,8851,9445,5681,3477,1105,142,241,12231,1003,3532,5009,1956,6008,11404,
  7377,2049,10968,12097,7591,5057,3445,4780,2920,7048,3127,8120,11279,6821,11502,8807,
  12138,2127,2839,3957,431,1579,6383,9784,5874,677,3336,6234,2766,1323,9115,12237,
  2031,6956,6413,2281,3969,3991,12133,9522,4737,10996,4774,5429,11871,3772,453,5908,
  2882,1805,2051,1954,11713,3963,2447,6142,8174,3030,1843,2361,12071,2908,3529,3434,
  3202,7796,2057,5369,11939,1512,6906,10474,11026,49,10806,5915,1489,9789,5942,10706,
  10431,7535,426,8974,3757,10314,9364,347,5868,9551,9634,6554,10596,9280,11566,174,
  2948,2503,6507,10723,11606,2459,64,3656,8455,5257,5919,7856,1747,9166,5486,9235,
  6065,835,3570,4240,11580,4046,10970,9139,1058,8210,11848,922,7967,1958,10211,1112,
  3728,4049,11130,5990,1404,325,948,11143,6190,295,11637,5766,8212,8273,2919,8527,
  6119,6992,8333,1360,2555,6167,1200,7105,7991,3329,9597,12121,5106,5961,10695,10327,
  3051,9923,4896,9326,81,3091,1000,7969,4611,726,1853,12149,4255,11112,2768,10654,
  1062,2294,3553,4805,2747,4846,8577,9154,1170,2319,790,11334,9275,9088,1326,5086,
  9094,6429,11077,10643,3504,3542,8668,9744,1479,1,8246,7143,11567,10984,4134,5736,
  4978,10938,5777,8961,4591,5728,6461,5023,9650,7468,949,9664,2975,11726,2744,9283,
  10092,5067,12171,2476,3748,11336,6522,827,9452,5374,12159,7935,3296,3949,9893,4452,
  10908,2525,3584,8112,8011,10616,4989,6958,11809,9447,12280,1022,11950,9821,11745,5791,
  5092,2089,9005,2881,3289,2013,9048,729,7901,1260,5755,4632,11955,2426,10593,1428,
  4890,5911,3932,9558,8830,3637,5542,145,5179,8595,3707,10530,355,3382,4231,9741,
  1207,9041,7012,1168,10146,11224,4645,11885,10911,10377,435,7952,4096,493,9908,6845,
  6039,2422,2187,9723,8643,9852,9302,6022,7278,1002,4284,5088,1607,7313,875,8509,
  9430,1045,2481,5012,7428,354,6591,9377,11847,2401,1067,7188,11516,390,8511,8456,
  7270,545,8585,9611,12047,1537,4143,4714,4885,1017,5084,1632,3066,27,1440,8526,
  9273,12046,11618,9289,3400,9890,3136,7098,8758,11813,7384,3985,11869,6730,10745,10111,
  2249,4048,2884,11136,2126,1630,9103,5407,2686,9042,2969,8311,9424,9919,8779,5332,
  10626,1777,4654,10863,7351,3636,9585,5291,8374,2166,4919,12176,9140,12129,7852,12286,
  4895,10805,2780,5195,2305,7247,9644,4053,10600,3364,3271,4057,4414,9442,7917,2174,
  3947,11951,2455,6599,10545,10975,3654,2894,7681,7126,7287,12269,4119,3343,2151,1522,
  7174,7350,11041,2442,2148,5959,6492,8330,8945,5598,3624,10397,1325,6565,1945,11260,
  10077,2674,3338,3276,11034,506,6505,1392,5478,8778,1178,2776,3408,10347,11124,2575,
  9489,12096,6092,10058,4167,6085,923,11251,11912,4578,10669,11914,425,10453,392,10104,
  8464,4235,8761,7376,2291,3375,7954,8896,6617,7790,1737,11667,3982,9342,6680,636,
  6825,7383,512,4670,2900,12050,7735,994,1687,11883,7021,146,10485,1403,5189,6094,
  2483,2054,3042,10945,3981,10821,11826,8882,8151,180,9600,7684,5219,10880,6780,204,
  11232,2600,7584,3121,3017,11053,7814,7043,4251,4739,11063,6771,7073,9261,2360,11925,
  1928,11825,8024,3678,3205,3359,11197,5209,8581,3238,8840,1136,9363,1826,3171,4489,
  7885,346,2068,1389,8257,3163,4840,6127,8062,8921,612,4238,10763,8067,125,11749,
  10125,5416,2110,716,9839,10584,11475,11873,3448,343,1908,4538,10423,7078,4727,1208,
  11572,3589,2982,1373,1721,10753,4103,2429,4209,5412,5993,9011,438,3515,7228,1218,
  8347,5232,8682,1327,7508,4924,448,1014,10029,12221,4566,5836,12229,2717,1535,3200,
  5588,5845,412,5102,7326,3744,3056,2528,7406,8314,9202,6454,6613,1417,10032,7784,
  1518,3765,4176,5063,9828,2275,6636,4267,6463,2065,7725,3495,8328,8755,8144,10533,
  5966,12077,9175,9520,5596,6302,8400,579,6781,11014,5734,11113,11164,4860,1131,10844,
  9068,8016,9694,3837,567,9348,7000,6627,7699,5082,682,11309,5207,4050,7087,844,
  7434,3769,293,9057,6940,9344,10883,2633,8190,3944,5530,5604,3480,2171,9282,11024,
  2213,8136,3805,767,12239,216,11520,6763,10353,7,8566,845,7235,3154,4360,3285,
  10268,2832,3572,1282,7559,3229,8360,10583,6105,3120,6643,6203,8536,8348,6919,3536,
  9199,10891,11463,5043,1658,5618,8787,5789,4719,751,11379,6389,10783,3065,7806,6586,
  2622,5386,510,7628,6921,578,10345,11839,8929,4684,12226,7154,9916,7302,8481,3670,
  11066,2334,1590,7878,10734,1802,1891,5103,6151,8820,3418,7846,9951,4693,417,9996,
  9652,4510,2946,5461,365,881,1927,1015,11675,11009,1371,12265,2485,11385,5039,6742,
  8449,1842,12217,8176,9577,4834,7937,9461,2643,11194,3045,6508,4094,3451,7911,11048,
  5406,4665,3020,6616,11345,7519,3669,5287,1790,7014,5410,11038,11249,2035,6125,10407,
  4565,7315,5078,10506,2840,2478,9270,4194,9195,4518,7469,1160,6878,2730,10421,10036,
  1734,3815,10939,5832,10595,10759,4423,8420,9617,7119,11010,11424,9173,189,10080,10526,
  3466,10588,7592,3578,11511,7785,9663,530,12150,8957,2532,3317,9349,10243,1481,9332,
  3454,3758,7899,4218,2593,11410,2276,982,6513,1849,8494,9021,4523,7988,8,457,
  648,150,8000,2307,2301,874,5650,170,9462,2873,9855,11498,2535,11169,5808,12268,
  9687,1901,7171,11787,3846,1573,6063,3793,466,11259,10608,3821,6320,4649,6263,2929};

/************************************************************
* Name:        psis_inv_montgomery
*
* Description: Contains inverses of powers of nth  root of -1 
*              divided by n in Montgomery domain with R=2^18
************************************************************/
uint16_t psis_inv_montgomery[NEWHOPE_N] = {
  256,10570,1510,7238,1034,7170,6291,7921,11665,3422,4000,2327,2088,5565,795,10647,
  1521,5484,2539,7385,1055,7173,8047,11683,1669,1994,3796,5809,4341,9398,11876,12230,
  10525,12037,12253,3506,4012,9351,4847,2448,7372,9831,3160,2207,5582,2553,7387,6322,
  9681,1383,10731,1533,219,5298,4268,7632,6357,9686,8406,4712,9451,10128,4958,5975,
  11387,8649,11769,6948,11526,12180,1740,10782,6807,2728,7412,4570,4164,4106,11120,12122,
  8754,11784,3439,5758,11356,6889,9762,11928,1704,1999,10819,12079,12259,7018,11536,1648,
  1991,2040,2047,2048,10826,12080,8748,8272,8204,1172,1923,7297,2798,7422,6327,4415,
  7653,6360,11442,12168,7005,8023,9924,8440,8228,2931,7441,1063,3663,5790,9605,10150,
  1450,8985,11817,10466,10273,12001,3470,7518,1074,1909,7295,9820,4914,702,5367,7789,
  8135,9940,1420,3714,11064,12114,12264,1752,5517,9566,11900,1700,3754,5803,829,1874,
  7290,2797,10933,5073,7747,8129,6428,6185,11417,1631,233,5300,9535,10140,11982,8734,
  8270,2937,10953,8587,8249,2934,9197,4825,5956,4362,9401,1343,3703,529,10609,12049,
  6988,6265,895,3639,4031,4087,4095,585,10617,8539,4731,4187,9376,3095,9220,10095,
  10220,1460,10742,12068,1724,5513,11321,6884,2739,5658,6075,4379,11159,10372,8504,4726,
  9453,3106,7466,11600,10435,8513,9994,8450,9985,3182,10988,8592,2983,9204,4826,2445,
  5616,6069,867,3635,5786,11360,5134,2489,10889,12089,1727,7269,2794,9177,1311,5454,
  9557,6632,2703,9164,10087,1441,3717,531,3587,2268,324,5313,759,1864,5533,2546,
  7386,9833,8427,4715,11207,1601,7251,4547,11183,12131,1733,10781,10318,1474,10744,5046,
  4232,11138,10369,6748,964,7160,4534,7670,8118,8182,4680,11202,6867,981,8918,1274,
  182,26,7026,8026,11680,12202,10521,1503,7237,4545,5916,9623,8397,11733,10454,3249,
  9242,6587,941,1890,270,10572,6777,9746,6659,6218,6155,6146,878,1881,7291,11575,
  12187,1741,7271,8061,11685,6936,4502,9421,4857,4205,7623,1089,10689,1527,8996,10063,
  11971,10488,6765,2722,3900,9335,11867,6962,11528,5158,4248,4118,5855,2592,5637,6072,
  2623,7397,8079,9932,4930,5971,853,3633,519,8852,11798,3441,11025,1575,225,8810,
  11792,12218,3501,9278,3081,9218,4828,7712,8124,11694,12204,3499,4011,573,3593,5780,
  7848,9899,10192,1456,208,7052,2763,7417,11593,10434,12024,8740,11782,10461,3250,5731,
  7841,9898,1414,202,3540,7528,2831,2160,10842,5060,4234,4116,588,84,12,7024,
  2759,9172,6577,11473,1639,9012,3043,7457,6332,11438,1634,1989,9062,11828,8712,11778,
  12216,10523,6770,9745,10170,4964,9487,6622,946,8913,6540,6201,4397,9406,8366,9973,
  8447,8229,11709,8695,10020,3187,5722,2573,10901,6824,4486,4152,9371,8361,2950,2177,
  311,1800,9035,8313,11721,3430,490,70,10,1757,251,3547,7529,11609,3414,7510,
  4584,4166,9373,1339,5458,7802,11648,1664,7260,9815,10180,6721,9738,10169,8475,8233,
  9954,1422,8981,1283,5450,11312,1616,3742,11068,10359,4991,713,3613,9294,8350,4704,
  672,96,7036,9783,11931,3460,5761,823,10651,12055,10500,1500,5481,783,3623,11051,
  8601,8251,8201,11705,10450,5004,4226,7626,2845,2162,3820,7568,9859,3164,452,10598,
  1514,5483,6050,6131,4387,7649,8115,6426,918,8909,8295,1185,5436,11310,8638,1234,
  5443,11311,5127,2488,2111,10835,5059,7745,2862,3920,560,80,1767,2008,3798,11076,
  6849,2734,10924,12094,8750,1250,10712,6797,971,7161,1023,8924,4786,7706,4612,4170,
  7618,6355,4419,5898,11376,10403,10264,6733,4473,639,5358,2521,9138,3061,5704,4326,
  618,5355,765,5376,768,7132,4530,9425,3102,9221,6584,11474,10417,10266,12000,6981,
  6264,4406,2385,7363,4563,4163,7617,9866,3165,9230,11852,10471,5007,5982,11388,5138,
  734,3616,11050,12112,6997,11533,12181,10518,12036,3475,2252,7344,9827,4915,9480,6621,
  4457,7659,9872,6677,4465,4149,7615,4599,657,3605,515,10607,6782,4480,640,1847,
  3775,5806,2585,5636,9583,1369,10729,8555,10000,11962,5220,7768,8132,8184,9947,1421,
  203,29,8782,11788,1684,10774,10317,4985,9490,8378,4708,11206,5112,5997,7879,11659,
  12199,8765,10030,4944,5973,6120,6141,6144,7900,11662,1666,238,34,3516,5769,9602,
  8394,9977,6692,956,10670,6791,9748,11926,8726,11780,5194,742,106,8793,10034,3189,
  10989,5081,4237,5872,4350,2377,10873,6820,6241,11425,10410,10265,3222,5727,9596,4882,
  2453,2106,3812,11078,12116,5242,4260,11142,8614,11764,12214,5256,4262,4120,11122,5100,
  11262,5120,2487,5622,9581,8391,8221,2930,10952,12098,6995,6266,9673,4893,699,3611,
  4027,5842,11368,1624,232,8811,8281,1183,169,8802,3013,2186,5579,797,3625,4029,
  11109,1587,7249,11569,8675,6506,2685,10917,12093,12261,12285,1755,7273,1039,1904,272,
  3550,9285,3082,5707,6082,4380,7648,11626,5172,4250,9385,8363,8217,4685,5936,848,
  8899,6538,934,1889,3781,9318,10109,10222,6727,961,5404,772,5377,9546,8386,1198,
  8949,3034,2189,7335,4559,5918,2601,10905,5069,9502,3113,7467,8089,11689,5181,9518,
  8382,2953,3933,4073,4093,7607,8109,2914,5683,4323,11151,1593,10761,6804,972,3650,
  2277,5592,4310,7638,9869,4921,703,1856,9043,4803,9464,1352,8971,11815,5199,7765,
  6376,4422,7654,2849,407,8836,6529,7955,2892,9191,1313,10721,12065,12257,1751,9028,
  8312,2943,2176,3822,546,78,8789,11789,10462,12028,6985,4509,9422,1346,5459,4291,
  613,10621,6784,9747,3148,7472,2823,5670,810,7138,8042,4660,7688,6365,6176,6149,
  2634,5643,9584,10147,11983,5223,9524,11894,10477,8519,1217,3685,2282,326,10580,3267,
  7489,4581,2410,5611,11335,6886,8006,8166,11700,3427,11023,8597,10006,3185,455,65,
  5276,7776,4622,5927,7869,9902,11948,5218,2501,5624,2559,10899,1557,1978,10816,10323,
  8497,4725,675,1852,10798,12076,10503,3256,9243,3076,2195,10847,12083,10504,12034,10497};

#else 
#error "NEWHOPE_N must be either 512 or 1024"
#endif
